Initial program 2.1
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
Applied simplify2.1
\[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{(\left(10 + k\right) \cdot k + 1)_*}}\]
- Using strategy
rm Applied associate-/l*2.2
\[\leadsto \color{blue}{\frac{{k}^{m}}{\frac{(\left(10 + k\right) \cdot k + 1)_*}{a}}}\]
Taylor expanded around 0 4.1
\[\leadsto \frac{{k}^{m}}{\color{blue}{\frac{1}{a} + \left(\frac{{k}^{2}}{a} + 10 \cdot \frac{k}{a}\right)}}\]
Applied simplify2.2
\[\leadsto \color{blue}{\frac{{k}^{m}}{(\left(\frac{k}{a}\right) \cdot k + \left((10 \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*\right))_*}}\]
- Using strategy
rm Applied add-cube-cbrt2.6
\[\leadsto \frac{{k}^{m}}{\color{blue}{\left(\sqrt[3]{(\left(\frac{k}{a}\right) \cdot k + \left((10 \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*\right))_*} \cdot \sqrt[3]{(\left(\frac{k}{a}\right) \cdot k + \left((10 \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*\right))_*}\right) \cdot \sqrt[3]{(\left(\frac{k}{a}\right) \cdot k + \left((10 \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*\right))_*}}}\]
Applied simplify2.6
\[\leadsto \frac{{k}^{m}}{\color{blue}{\left(\sqrt[3]{(\left(k + 10\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*} \cdot \sqrt[3]{(\left(k + 10\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*}\right)} \cdot \sqrt[3]{(\left(\frac{k}{a}\right) \cdot k + \left((10 \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*\right))_*}}\]
Applied simplify0.7
\[\leadsto \frac{{k}^{m}}{\left(\sqrt[3]{(\left(k + 10\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*} \cdot \sqrt[3]{(\left(k + 10\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*}\right) \cdot \color{blue}{\sqrt[3]{(\left(k + 10\right) \cdot \left(\frac{k}{a}\right) + \left(\frac{1}{a}\right))_*}}}\]
